Re: Population SD when sample size > 20?

Kevin E. Thorpe wrote:

Data Matter wrote:

I'd advise consulting a real statistics textbook. the information on
this web page is rather dubious.

I agree.

The meaning of SD is given as "measurement of the spread in individual
data points to reflect the uncertainty of a single measurement". One
of the worst definitions I have ever seen. What is this "single
measurement"?

The reason why you would need to take a sample is because it is
impractical or unrealistic or impossible or too costly to measure all
units of a population. As such, the population mean or population SD
should be treated as unknowable whenever your data contain a sample of
that population. It is then irrelevant what the formula is.

In the case where you can measure every item in a population (i.e. the
population is finite, and realistically small), then you can use the
population mean/SD formulas with N as the denominator.

The estimator using n-1 is commonly known as the unbiased
estimate of the population sd (or variance if you drop the
square root). On the other hand, a divisor of n gives you
the maximum likelihood estimate of the population sd.

I should correct myself. It is the MLE under the assumption
of normality.

I don't like these "rules of thumb" that seem so popular.
They discourage intelligent thought.


DM

PS. It gets worse as you go further down the page... everything it says
about "standard error of the mean" is wrong.

The statements about confidence intervals are also suspect.


--
Kevin E. Thorpe
Assistant Professor, Department of Public Health Sciences
Faculty of Medicine, University of Toronto

.

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